Are you sure it's the cabinets fitted at different heights at not an optical annoyance caused by the extra tiling above the cabinets on one side?
We had this in a bathroom in an old place we lived in.
Tiler drew a level line the whole way around the room based on the level position of the bath.
You could do a similar level line based on say, the level of the worktop.
However, by the time the tiler got to the top of our bathroom walls there was a difference on two of the four sides.
That is (it was an old building) either the walls were sloping, so in effect were longer to reach the ceiling or the plastering on the ceiling was uneven, leaving a gap at the top of two walls.
Maybe through historical settlement of walls and so on.
I wouldn't have thought a 10mm difference was much in an old house - ours was about 4/5 cm.
The key thing is disguising it. If you tile down from the ceiling and keep the cut tile above the new units you'll probably never notice the disparity but obviously, if you tile up to the ceiling and fill the gap with a cut tile, then you see it!
Personally, I would imagine the units are more likely level and your walls are out of whack - but I'm an optimist!
Could he just re-do the tiles above the units and hide the 'cut' somehow where the tiles reach the unit.
You can blame the tiler/fitter but he probably wouldn't have realised until he got nearer the ceiling, that there was going to be a gap but I feel your pain - it's annoying